Possible but no guarantee - probably more unlikely than likely.
Best you finish the Premiere Elements 3.0/3.0.2 project in Premiere Elements 3.0/3.0.2. (Wherever the case, please use version 3 as the 3.0.2 Update.)
Go with the free 30 day tryout of Premiere Elements 12 from Adobe before purchase. During that time, copy one of the version 3 projects, and try to open it in Premiere Elements 12. Remember, once you edit a project created in an earlier program and then open and edit it in a later program, you cannot go back and edit the later version edited project in the earlier program.
Best give the tryout a work out to assure that it is compatible with your computer environment and meets all your video editing needs. Annually (around September) Adobe has been releasing a new version of Premiere Elements. No one knows what the new features will be of the new release until its moment of release.